I want your feedback to make the book better for you and other readers. If you find typos, errors, or places where the text may be improved, please let me know. The best ways to provide feedback are by GitHub or hypothes.is annotations.
You can leave a comment at the bottom of the page/chapter, or open an issue or submit a pull request on GitHub: https://github.com/isaactpetersen/Fantasy-Football-Analytics-Textbook
Alternatively, you can leave an annotation using hypothes.is.
To add an annotation, select some text and then click the
symbol on the pop-up menu.
To see the annotations of others, click the
symbol in the upper right-hand corner of the page.
19 Machine Learning
19.1 Getting Started
19.1.1 Load Packages
19.1.2 Load Data
Code
# Downloaded Data - Processed
load(file = "./data/nfl_players.RData")
load(file = "./data/nfl_teams.RData")
load(file = "./data/nfl_rosters.RData")
load(file = "./data/nfl_rosters_weekly.RData")
load(file = "./data/nfl_schedules.RData")
load(file = "./data/nfl_combine.RData")
load(file = "./data/nfl_draftPicks.RData")
load(file = "./data/nfl_depthCharts.RData")
load(file = "./data/nfl_pbp.RData")
load(file = "./data/nfl_4thdown.RData")
load(file = "./data/nfl_participation.RData")
#load(file = "./data/nfl_actualFantasyPoints_weekly.RData")
load(file = "./data/nfl_injuries.RData")
load(file = "./data/nfl_snapCounts.RData")
load(file = "./data/nfl_espnQBR_seasonal.RData")
load(file = "./data/nfl_espnQBR_weekly.RData")
load(file = "./data/nfl_nextGenStats_weekly.RData")
load(file = "./data/nfl_advancedStatsPFR_seasonal.RData")
load(file = "./data/nfl_advancedStatsPFR_weekly.RData")
load(file = "./data/nfl_playerContracts.RData")
load(file = "./data/nfl_ftnCharting.RData")
load(file = "./data/nfl_playerIDs.RData")
load(file = "./data/nfl_rankings_draft.RData")
load(file = "./data/nfl_rankings_weekly.RData")
load(file = "./data/nfl_expectedFantasyPoints_weekly.RData")
load(file = "./data/nfl_expectedFantasyPoints_pbp.RData")
# Calculated Data - Processed
load(file = "./data/nfl_actualStats_career.RData")
load(file = "./data/nfl_actualStats_seasonal.RData")
load(file = "./data/player_stats_weekly.RData")
load(file = "./data/player_stats_seasonal.RData")19.1.3 Specify Options
19.2 Overview of Machine Learning
Machine learning takes us away from focusing on causal inference. Machine learning does not care about which processes are causal—i.e., which processes influence the outcome. Instead, machine learning cares about prediction—it cares about a predictor variable to the extent that it increases predictive accuracy regardless of whether it is causally related to the outcome.
Machine learning can be useful for leveraging big data and lots of predictor variable to develop predictive models with greater accuracy. However, many machine learning techniques are black boxes—it is often unclear how or why certain predictions are made, which can make it difficult to interpret the model’s decisions and understand the underlying relationships between variables. Machine learning tends to be a data-driven, atheoretical technique. This can result in overfitting. Thus, when estimating machine learning models, it is common to keep a hold-out sample for use in cross-validation to evaluate the extent of shrinkage of model coefficients. The data that the model is trained on is known as the “training data”. The data that the model was not trained on but is then is independently tested on—i.e., the hold-out sample—is the “test data”. Shrinkage occurs when predictor variables explain some random error variance in the original model. When the model is applied to an independent sample (i.e., the test data), the predictive model will likely not perform quite as well, and the regressions coefficients will tend to get smaller (i.e., shrink).
If the test data were collected as part of the same processes as the original data and were merely held out for purposes of analysis, this is called internal cross-validation. If the test data were collected separately from the original data used to train the model, this is called external cross-validation.
Most machine learning methods were developed with cross-sectional data in mind. That is, they assume that each person has only one observation on the outcome variable. However, with longitudinal data, each person has multiple observations on the outcome variable.
When performing machine learning, various approaches may help address this:
- transform data from long to wide form, so that each person has only one row
- when designing the training and test sets, keep all measurements from the same person in the same data object (either the training or test set); do not have some measurements from a given person in the training set and other measurements from the same person in the test set
- use a machine learning approach that accounts for the clustered/nested nature of the data
19.3 Types of Machine Learning
There are many approaches to machine learning. This chapter discusses several key ones:
- supervised learning
- continuous outcome (i.e., regression)
- linear regression
- lasso regression
- ridge regression
- elastic net regression
- categorical outcome (i.e., classification)
- logistic regression
- support vector machine
- random forest
- extreme gradient boosting
- continuous outcome (i.e., regression)
- unsupervised learning
- clustering
- principal component analysis
- semi-supervised learning
- reinforcement learning
- deep learning
- ensemble
Ensemble machine learning methods combine multiple machine learning approaches with the goal that combining multiple approaches might lead to more accurate predictions that any one method might be able to achieve on its own.
19.3.1 Supervised Learning
[DEFINE SUPERVISED LEARNING]
Unlike linear and logistic regression, various machine learning techniques can handle multicollinearity, including LASSO regression, ridge regression, and elastic net regression. Least absolute shrinkage and selection operator (LASSO) regression helps perform selection of which predictor variables to keep in the model by shrinking some coefficients to zero. Ridge regression shrinks the coefficients of predictor variables toward zero, but not to zero, so it does not perform selection of which predictor variables to retain; this allows it to allow nonzero coefficients for multiple correlated predictor variables in the context of multicollinearity. Elastic net involves a combination of LASSO and ridge regression; it performs selection of which predictor variables to keep by shrinking the coefficients of some predictor variables to zero, and it shrinks the coefficients of some predictor variables toward zero, to address multicollinearity.
Unless interactions or nonlinear terms are specified, linear, logistic, LASSO, ridge, and elastic net regresstion do not account for interactions among the predictor variables or for nonlinear associations between the predictor variables and the outcome variable. By contrast, random forests and extreme gradient boosting do account for interactions among the predictor variables and for nonlinear associations between the predictor variables and the outcome variable.
19.3.2 Unsupervised Learning
[DEFINE UNSUPERVISED LEARNING]
We describe cluster analysis in Chapter 21. We describe principal component analysis in Chapter 23.
19.3.3 Semi-supervised Learning
[DEFINE SEMI-SUPERVISED LEARNING]
19.3.4 Reinforcement Learning
[DEFINE REINFORCEMENT LEARNING]
19.4 Data Processing
19.4.1 Prepare Data for Merging
Code
# Prepare data for merging
#-todo: calculate years_of_experience
## Use common name for the same (gsis_id) ID variable
#nfl_actualFantasyPoints_player_weekly <- nfl_actualFantasyPoints_player_weekly %>%
# rename(gsis_id = player_id)
#
#nfl_actualFantasyPoints_player_seasonal <- nfl_actualFantasyPoints_player_seasonal %>%
# rename(gsis_id = player_id)
player_stats_seasonal_offense <- player_stats_seasonal %>%
filter(position_group %in% c("QB","RB","WR","TE")) %>%
rename(gsis_id = player_id)
player_stats_weekly_offense <- player_stats_weekly %>%
filter(position_group %in% c("QB","RB","WR","TE")) %>%
rename(gsis_id = player_id)
nfl_expectedFantasyPoints_weekly <- nfl_expectedFantasyPoints_weekly %>%
rename(gsis_id = player_id)
## Rename other variables to ensure common names
## Ensure variables with the same name have the same type
nfl_players <- nfl_players %>%
mutate(
birth_date = as.Date(birth_date),
jersey_number = as.character(jersey_number),
gsis_it_id = as.character(gsis_it_id),
years_of_experience = as.integer(years_of_experience))
player_stats_seasonal_offense <- player_stats_seasonal_offense %>%
mutate(
birth_date = as.Date(birth_date),
jersey_number = as.character(jersey_number),
gsis_it_id = as.character(gsis_it_id))
nfl_rosters <- nfl_rosters %>%
mutate(
draft_number = as.integer(draft_number))
nfl_rosters_weekly <- nfl_rosters_weekly %>%
mutate(
draft_number = as.integer(draft_number))
nfl_depthCharts <- nfl_depthCharts %>%
mutate(
season = as.integer(season))
nfl_expectedFantasyPoints_weekly <- nfl_expectedFantasyPoints_weekly %>%
mutate(
season = as.integer(season),
receptions = as.integer(receptions)) %>%
distinct(gsis_id, season, week, .keep_all = TRUE) # drop duplicated rows
## Rename variables
nfl_draftPicks <- nfl_draftPicks %>%
rename(
games_career = games,
pass_completions_career = pass_completions,
pass_attempts_career = pass_attempts,
pass_yards_career = pass_yards,
pass_tds_career = pass_tds,
pass_ints_career = pass_ints,
rush_atts_career = rush_atts,
rush_yards_career = rush_yards,
rush_tds_career = rush_tds,
receptions_career = receptions,
rec_yards_career = rec_yards,
rec_tds_career = rec_tds,
def_solo_tackles_career = def_solo_tackles,
def_ints_career = def_ints,
def_sacks_career = def_sacks
)
## Subset variables
nfl_expectedFantasyPoints_weekly <- nfl_expectedFantasyPoints_weekly %>%
select(gsis_id:position, contains("_exp"), contains("_diff"), contains("_team")) #drop "raw stats" variables (e.g., rec_yards_gained) so they don't get coalesced with actual stats
# Check duplicate ids
player_stats_seasonal_offense %>%
group_by(gsis_id, season) %>%
filter(n() > 1) %>%
head()Code
Identify objects with shared variable names:
[1] "gsis_id" "position"
[1] 21360
[1] 2855
[1] "gsis_id" "season" "team" "age"
[1] 14859
[1] 10395
[1] 14858
[1] 10395
[1] 14859
[1] 10325
[1] "gsis_id" "season" "week" "position" "full_name"
[1] 845134
[1] 100272
[1] 841942
[1] 100272
[1] 845101
[1] 97815
[1] 845118
[1] 97815
19.4.2 Merge Data
To merge data, we use the powerjoin package (Fabri, 2022):
Code
# Create lists of objects to merge, depending on data structure: id; or id-season; or id-season-week
#-todo: remove redundant variables
playerListToMerge <- list(
nfl_players %>% filter(!is.na(gsis_id)),
nfl_draftPicks %>% filter(!is.na(gsis_id)) %>% select(-season)
)
playerSeasonListToMerge <- list(
player_stats_seasonal_offense %>% filter(!is.na(gsis_id), !is.na(season)),
nfl_advancedStatsPFR_seasonal %>% filter(!is.na(gsis_id), !is.na(season))
)
playerSeasonWeekListToMerge <- list(
nfl_rosters_weekly %>% filter(!is.na(gsis_id), !is.na(season), !is.na(week)),
#nfl_actualStats_offense_weekly,
nfl_expectedFantasyPoints_weekly %>% filter(!is.na(gsis_id), !is.na(season), !is.na(week))
#nfl_advancedStatsPFR_weekly,
)
playerSeasonWeekPositionListToMerge <- list(
nfl_depthCharts %>% filter(!is.na(gsis_id), !is.na(season), !is.na(week))
)
# Merge data
playerMerged <- playerListToMerge %>%
reduce(
powerjoin::power_full_join,
by = c("gsis_id"),
conflict = coalesce_xy) # where the objects have the same variable name (e.g., position), keep the values from object 1, unless it's NA, in which case use the relevant value from object 2
playerSeasonMerged <- playerSeasonListToMerge %>%
reduce(
powerjoin::power_full_join,
by = c("gsis_id","season"),
conflict = coalesce_xy) # where the objects have the same variable name (e.g., team), keep the values from object 1, unless it's NA, in which case use the relevant value from object 2
playerSeasonWeekMerged <- playerSeasonWeekListToMerge %>%
reduce(
powerjoin::power_full_join,
by = c("gsis_id","season","week"),
conflict = coalesce_xy) # where the objects have the same variable name (e.g., position), keep the values from object 1, unless it's NA, in which case use the relevant value from object 2Identify objects with shared variable names:
[1] "gsis_id" "position"
[3] "position_group" "first_name"
[5] "last_name" "esb_id"
[7] "display_name" "rookie_year"
[9] "college_conference" "current_team_id"
[11] "draft_club" "draft_number"
[13] "draftround" "entry_year"
[15] "football_name" "gsis_it_id"
[17] "headshot" "jersey_number"
[19] "short_name" "smart_id"
[21] "status" "status_description_abbr"
[23] "status_short_description" "uniform_number"
[25] "height" "weight"
[27] "college_name" "birth_date"
[29] "suffix" "years_of_experience"
[31] "pfr_player_name" "team"
[33] "age"
Code
seasonalData <- powerjoin::power_full_join(
playerSeasonMerged,
playerMerged %>% select(-age, -years_of_experience, -team, -team_abbr, -team_seq, -current_team_id), # drop variables from id objects that change from year to year (and thus are not necessarily accurate for a given season)
by = "gsis_id",
conflict = coalesce_xy # where the objects have the same variable name (e.g., position), keep the values from object 1, unless it's NA, in which case use the relevant value from object 2
) %>%
filter(!is.na(season)) %>%
select(gsis_id, season, player_display_name, position, team, games, everything()) [1] "gsis_id" "season"
[3] "week" "team"
[5] "jersey_number" "status"
[7] "first_name" "last_name"
[9] "birth_date" "height"
[11] "weight" "college"
[13] "pfr_id" "headshot_url"
[15] "status_description_abbr" "football_name"
[17] "esb_id" "gsis_it_id"
[19] "smart_id" "entry_year"
[21] "rookie_year" "draft_club"
[23] "draft_number" "position"
Code
seasonalAndWeeklyData <- powerjoin::power_full_join(
playerSeasonWeekMerged,
seasonalData,
by = c("gsis_id","season"),
conflict = coalesce_xy # where the objects have the same variable name (e.g., position), keep the values from object 1, unless it's NA, in which case use the relevant value from object 2
) %>%
filter(!is.na(week)) %>%
select(gsis_id, season, week, full_name, position, team, everything())19.4.3 Additional Processing
19.4.4 Fill in Missing Data for Static Variables
19.4.5 Lag Fantasy Points
19.4.6 Subset to Predictor Variables and Outcome Variable
Code
dropVars <- c(
"birth_date", "loaded", "full_name", "player_name", "player_display_name", "display_name", "suffix", "headshot_url", "player", "pos",
"espn_id", "sportradar_id", "yahoo_id", "rotowire_id", "pff_id", "fantasy_data_id", "sleeper_id", "pfr_id",
"pfr_player_id", "cfb_player_id", "pfr_player_name", "esb_id", "gsis_it_id", "smart_id",
"college", "college_name", "team_abbr", "current_team_id", "college_conference", "draft_club", "status_description_abbr",
"status_short_description", "short_name", "headshot", "uniform_number", "jersey_number", "first_name", "last_name",
"football_name", "team")
seasonalData_lag_subset <- seasonalData_lag %>%
dplyr::select(-any_of(dropVars))19.4.7 Separate by Position
Code
seasonalData_lag_subsetQB <- seasonalData_lag_subset %>%
filter(position == "QB") %>%
select(
gsis_id, season, games, gs, years_of_experience, age, ageCentered20, ageCentered20Quadratic,
height, weight, rookie_year, draft_number,
fantasy_points, fantasy_points_ppr, fantasyPoints, fantasyPoints_lag,
completions:rushing_2pt_conversions, special_teams_tds, contains(".pass"), contains(".rush"))
seasonalData_lag_subsetRB <- seasonalData_lag_subset %>%
filter(position == "RB") %>%
select(
gsis_id, season, games, gs, years_of_experience, age, ageCentered20, ageCentered20Quadratic,
height, weight, rookie_year, draft_number,
fantasy_points, fantasy_points_ppr, fantasyPoints, fantasyPoints_lag,
carries:special_teams_tds, contains(".rush"), contains(".rec"))
seasonalData_lag_subsetWR <- seasonalData_lag_subset %>%
filter(position == "WR") %>%
select(
gsis_id, season, games, gs, years_of_experience, age, ageCentered20, ageCentered20Quadratic,
height, weight, rookie_year, draft_number,
fantasy_points, fantasy_points_ppr, fantasyPoints, fantasyPoints_lag,
carries:special_teams_tds, contains(".rush"), contains(".rec"))
seasonalData_lag_subsetTE <- seasonalData_lag_subset %>%
filter(position == "TE") %>%
select(
gsis_id, season, games, gs, years_of_experience, age, ageCentered20, ageCentered20Quadratic,
height, weight, rookie_year, draft_number,
fantasy_points, fantasy_points_ppr, fantasyPoints, fantasyPoints_lag,
carries:special_teams_tds, contains(".rush"), contains(".rec"))19.4.8 Split into Test and Training Data
Code
seasonalData_lag_qb_all <- seasonalData_lag_subsetQB
seasonalData_lag_rb_all <- seasonalData_lag_subsetRB
seasonalData_lag_wr_all <- seasonalData_lag_subsetWR
seasonalData_lag_te_all <- seasonalData_lag_subsetTE
set.seed(52242) # for reproducibility (to keep the same train/holdout players)
activeQBs <- unique(seasonalData_lag_qb_all$gsis_id[which(seasonalData_lag_qb_all$season == max(seasonalData_lag_qb_all$season, na.rm = TRUE))])
retiredQBs <- unique(seasonalData_lag_qb_all$gsis_id[which(seasonalData_lag_qb_all$gsis_id %ni% activeQBs)])
numQBs <- length(unique(seasonalData_lag_qb_all$gsis_id))
qbHoldoutIDs <- sample(retiredQBs, size = ceiling(.2 * numQBs)) # holdout 20% of players
activeRBs <- unique(seasonalData_lag_rb_all$gsis_id[which(seasonalData_lag_rb_all$season == max(seasonalData_lag_rb_all$season, na.rm = TRUE))])
retiredRBs <- unique(seasonalData_lag_rb_all$gsis_id[which(seasonalData_lag_rb_all$gsis_id %ni% activeRBs)])
numRBs <- length(unique(seasonalData_lag_rb_all$gsis_id))
rbHoldoutIDs <- sample(retiredRBs, size = ceiling(.2 * numRBs)) # holdout 20% of players
set.seed(52242) # for reproducibility (to keep the same train/holdout players); added here to prevent a downstream error with predict.missRanger() due to missingness; this suggests that an error can arise from including a player in the holdout sample who has missingness in particular variables; would be good to identify which player(s) in the holdout sample evoke that error to identify the kinds of missingness that yield the error
activeWRs <- unique(seasonalData_lag_wr_all$gsis_id[which(seasonalData_lag_wr_all$season == max(seasonalData_lag_wr_all$season, na.rm = TRUE))])
retiredWRs <- unique(seasonalData_lag_wr_all$gsis_id[which(seasonalData_lag_wr_all$gsis_id %ni% activeWRs)])
numWRs <- length(unique(seasonalData_lag_wr_all$gsis_id))
wrHoldoutIDs <- sample(retiredWRs, size = ceiling(.2 * numWRs)) # holdout 20% of players
activeTEs <- unique(seasonalData_lag_te_all$gsis_id[which(seasonalData_lag_te_all$season == max(seasonalData_lag_te_all$season, na.rm = TRUE))])
retiredTEs <- unique(seasonalData_lag_te_all$gsis_id[which(seasonalData_lag_te_all$gsis_id %ni% activeTEs)])
numTEs <- length(unique(seasonalData_lag_te_all$gsis_id))
teHoldoutIDs <- sample(retiredTEs, size = ceiling(.2 * numTEs)) # holdout 20% of players
seasonalData_lag_qb_train <- seasonalData_lag_qb_all %>%
filter(gsis_id %ni% qbHoldoutIDs)
seasonalData_lag_qb_test <- seasonalData_lag_qb_all %>%
filter(gsis_id %in% qbHoldoutIDs)
seasonalData_lag_rb_train <- seasonalData_lag_rb_all %>%
filter(gsis_id %ni% rbHoldoutIDs)
seasonalData_lag_rb_test <- seasonalData_lag_rb_all %>%
filter(gsis_id %in% rbHoldoutIDs)
seasonalData_lag_wr_train <- seasonalData_lag_wr_all %>%
filter(gsis_id %ni% wrHoldoutIDs)
seasonalData_lag_wr_test <- seasonalData_lag_wr_all %>%
filter(gsis_id %in% wrHoldoutIDs)
seasonalData_lag_te_train <- seasonalData_lag_te_all %>%
filter(gsis_id %ni% teHoldoutIDs)
seasonalData_lag_te_test <- seasonalData_lag_te_all %>%
filter(gsis_id %in% teHoldoutIDs)19.4.9 Impute the Missing Data
Here is a vignette demonstrating how to impute missing data using missForest(): https://rpubs.com/lmorgan95/MissForest (archived at: https://perma.cc/6GB4-2E22). Below, we impute the training data (and all data) separately by position. We then use the imputed training data to make out-of-sample predictions to fill in the missing data for the testing data. We do not want to impute the training and testing data together so that we can keep them separate for the purposes of cross-validation. However, we impute all data (training and test data together) for purposes of making out-of-sample predictions from the machine learning models to predict players’ performance next season (when actuals are not yet available for evaluating their accuracy). To impute data, we use the missRanger package (Mayer, 2024).
Note: the following code takes a while to run.
Code
Variables to impute: fantasy_points, fantasy_points_ppr, special_teams_tds, passing_epa, pacr, rushing_epa, fantasyPoints_lag, passing_cpoe, rookie_year, draft_number, gs, pass_attempts.pass, throwaways.pass, spikes.pass, drops.pass, bad_throws.pass, times_blitzed.pass, times_hurried.pass, times_hit.pass, times_pressured.pass, batted_balls.pass, on_tgt_throws.pass, rpo_plays.pass, rpo_yards.pass, rpo_pass_att.pass, rpo_pass_yards.pass, rpo_rush_att.pass, rpo_rush_yards.pass, pa_pass_att.pass, pa_pass_yards.pass, att.rush, yds.rush, td.rush, x1d.rush, ybc.rush, yac.rush, brk_tkl.rush, att_br.rush, drop_pct.pass, bad_throw_pct.pass, on_tgt_pct.pass, pressure_pct.pass, ybc_att.rush, yac_att.rush, pocket_time.pass
Variables used to impute: gsis_id, season, games, gs, years_of_experience, age, ageCentered20, ageCentered20Quadratic, height, weight, rookie_year, draft_number, fantasy_points, fantasy_points_ppr, fantasyPoints, fantasyPoints_lag, completions, attempts, passing_yards, passing_tds, passing_interceptions, sacks_suffered, sack_yards_lost, sack_fumbles, sack_fumbles_lost, passing_air_yards, passing_yards_after_catch, passing_first_downs, passing_epa, passing_cpoe, passing_2pt_conversions, pacr, carries, rushing_yards, rushing_tds, rushing_fumbles, rushing_fumbles_lost, rushing_first_downs, rushing_epa, rushing_2pt_conversions, special_teams_tds, pocket_time.pass, pass_attempts.pass, throwaways.pass, spikes.pass, drops.pass, bad_throws.pass, times_blitzed.pass, times_hurried.pass, times_hit.pass, times_pressured.pass, batted_balls.pass, on_tgt_throws.pass, rpo_plays.pass, rpo_yards.pass, rpo_pass_att.pass, rpo_pass_yards.pass, rpo_rush_att.pass, rpo_rush_yards.pass, pa_pass_att.pass, pa_pass_yards.pass, drop_pct.pass, bad_throw_pct.pass, on_tgt_pct.pass, pressure_pct.pass, ybc_att.rush, yac_att.rush, att.rush, yds.rush, td.rush, x1d.rush, ybc.rush, yac.rush, brk_tkl.rush, att_br.rush
fntsy_ fnts__ spcl__ pssng_p pacr rshng_ fntsP_ pssng_c rok_yr drft_n gs pss_t. thrww. spks.p drps.p bd_th. tms_b. tms_hr. tms_ht. tms_p. bttd_. on_tgt_t. rp_pl. rp_yr. rp_pss_t. rp_pss_y. rp_rsh_t. rp_rsh_y. p_pss_t. p_pss_y. att.rs yds.rs td.rsh x1d.rs ybc.rs yc.rsh brk_t. att_b. drp_p. bd_t_. on_tgt_p. prss_. ybc_t. yc_tt. pckt_.
iter 1: 0.0054 0.0024 0.7924 0.1919 0.7612 0.3628 0.4789 0.4133 0.0224 0.5216 0.0271 0.0134 0.3024 0.7659 0.1304 0.0541 0.0758 0.1759 0.1820 0.0370 0.3238 0.0291 0.2952 0.1812 0.0885 0.0867 0.2627 0.2563 0.1093 0.0902 0.0580 0.0645 0.1732 0.0524 0.0578 0.1795 0.3524 0.3428 0.7447 0.5158 0.0824 0.6803 0.3529 0.5758 0.8111
iter 2: 0.0044 0.0048 0.8304 0.2002 0.7926 0.3736 0.4801 0.4289 0.0488 0.6139 0.0188 0.0090 0.2883 0.7481 0.0764 0.0385 0.0718 0.1231 0.1329 0.0337 0.2760 0.0113 0.0548 0.0814 0.0765 0.0990 0.1989 0.2841 0.0707 0.0952 0.0396 0.0386 0.1606 0.0492 0.0525 0.1220 0.2541 0.3556 0.7468 0.4937 0.0827 0.6610 0.3465 0.5796 0.8134
iter 3: 0.0049 0.0046 0.8690 0.1986 0.7810 0.3641 0.4774 0.4360 0.0528 0.6123 0.0188 0.0088 0.2867 0.7538 0.0767 0.0393 0.0734 0.1261 0.1374 0.0343 0.2741 0.0119 0.0524 0.0816 0.0748 0.1008 0.2184 0.2811 0.0691 0.0926 0.0389 0.0413 0.1640 0.0511 0.0585 0.1255 0.2510 0.3609 0.7477 0.5108 0.0858 0.6426 0.3588 0.5734 0.8300
missRanger object. Extract imputed data via $data
- best iteration: 2
- best average OOB imputation error: 0.2524825
Code
data_all_qb <- seasonalData_lag_qb_all_imp$data
data_all_qb$fantasyPointsMC_lag <- scale(data_all_qb$fantasyPoints_lag, scale = FALSE) # mean-centered
data_all_qb_matrix <- data_all_qb %>%
mutate(across(where(is.factor), ~ as.numeric(as.integer(.)))) %>%
as.matrix()
newData_qb <- data_all_qb %>%
filter(season == max(season, na.rm = TRUE)) %>%
select(-fantasyPoints_lag, -fantasyPointsMC_lag)
newData_qb_matrix <- data_all_qb_matrix[
data_all_qb_matrix[, "season"] == max(data_all_qb_matrix[, "season"], na.rm = TRUE), # keep only rows with the most recent season
, # all columns
drop = FALSE]
dropCol_qb <- which(colnames(newData_qb_matrix) %in% c("fantasyPoints_lag","fantasyPointsMC_lag"))
newData_qb_matrix <- newData_qb_matrix[, -dropCol_qb, drop = FALSE]
seasonalData_lag_qb_train_imp <- missRanger::missRanger(
seasonalData_lag_qb_train,
pmm.k = 5,
verbose = 2,
seed = 52242,
keep_forests = TRUE)
Variables to impute: fantasy_points, fantasy_points_ppr, special_teams_tds, passing_epa, pacr, rushing_epa, fantasyPoints_lag, passing_cpoe, rookie_year, draft_number, gs, pass_attempts.pass, throwaways.pass, spikes.pass, drops.pass, bad_throws.pass, times_blitzed.pass, times_hurried.pass, times_hit.pass, times_pressured.pass, batted_balls.pass, on_tgt_throws.pass, rpo_plays.pass, rpo_yards.pass, rpo_pass_att.pass, rpo_pass_yards.pass, rpo_rush_att.pass, rpo_rush_yards.pass, pa_pass_att.pass, pa_pass_yards.pass, att.rush, yds.rush, td.rush, x1d.rush, ybc.rush, yac.rush, brk_tkl.rush, att_br.rush, drop_pct.pass, bad_throw_pct.pass, on_tgt_pct.pass, pressure_pct.pass, ybc_att.rush, yac_att.rush, pocket_time.pass
Variables used to impute: gsis_id, season, games, gs, years_of_experience, age, ageCentered20, ageCentered20Quadratic, height, weight, rookie_year, draft_number, fantasy_points, fantasy_points_ppr, fantasyPoints, fantasyPoints_lag, completions, attempts, passing_yards, passing_tds, passing_interceptions, sacks_suffered, sack_yards_lost, sack_fumbles, sack_fumbles_lost, passing_air_yards, passing_yards_after_catch, passing_first_downs, passing_epa, passing_cpoe, passing_2pt_conversions, pacr, carries, rushing_yards, rushing_tds, rushing_fumbles, rushing_fumbles_lost, rushing_first_downs, rushing_epa, rushing_2pt_conversions, special_teams_tds, pocket_time.pass, pass_attempts.pass, throwaways.pass, spikes.pass, drops.pass, bad_throws.pass, times_blitzed.pass, times_hurried.pass, times_hit.pass, times_pressured.pass, batted_balls.pass, on_tgt_throws.pass, rpo_plays.pass, rpo_yards.pass, rpo_pass_att.pass, rpo_pass_yards.pass, rpo_rush_att.pass, rpo_rush_yards.pass, pa_pass_att.pass, pa_pass_yards.pass, drop_pct.pass, bad_throw_pct.pass, on_tgt_pct.pass, pressure_pct.pass, ybc_att.rush, yac_att.rush, att.rush, yds.rush, td.rush, x1d.rush, ybc.rush, yac.rush, brk_tkl.rush, att_br.rush
fntsy_ fnts__ spcl__ pssng_p pacr rshng_ fntsP_ pssng_c rok_yr drft_n gs pss_t. thrww. spks.p drps.p bd_th. tms_b. tms_hr. tms_ht. tms_p. bttd_. on_tgt_t. rp_pl. rp_yr. rp_pss_t. rp_pss_y. rp_rsh_t. rp_rsh_y. p_pss_t. p_pss_y. att.rs yds.rs td.rsh x1d.rs ybc.rs yc.rsh brk_t. att_b. drp_p. bd_t_. on_tgt_p. prss_. ybc_t. yc_tt. pckt_.
iter 1: 0.0061 0.0028 0.8162 0.1897 0.5083 0.3633 0.4726 0.4456 0.0242 0.4723 0.0283 0.0141 0.2939 0.7728 0.1343 0.0558 0.0744 0.1757 0.1818 0.0381 0.3288 0.0351 0.2921 0.1846 0.0860 0.0894 0.2737 0.2661 0.1127 0.0900 0.0586 0.0644 0.1800 0.0574 0.0639 0.1792 0.3570 0.3486 0.7646 0.5313 0.0868 0.7084 0.3533 0.5933 0.8466
iter 2: 0.0052 0.0052 0.8304 0.1937 0.5621 0.3715 0.4614 0.4586 0.0505 0.5647 0.0192 0.0092 0.2953 0.7530 0.0800 0.0393 0.0725 0.1170 0.1355 0.0343 0.2771 0.0121 0.0555 0.0731 0.0713 0.0979 0.2073 0.2943 0.0698 0.0911 0.0416 0.0399 0.1683 0.0527 0.0577 0.1262 0.2474 0.3582 0.7719 0.5165 0.0900 0.6862 0.3642 0.5926 0.8400
iter 3: 0.0053 0.0051 0.8261 0.2008 0.5551 0.3571 0.4727 0.4410 0.0551 0.5658 0.0188 0.0092 0.2859 0.7460 0.0807 0.0402 0.0739 0.1202 0.1393 0.0351 0.2808 0.0114 0.0595 0.0705 0.0775 0.1051 0.2163 0.2935 0.0718 0.0921 0.0426 0.0400 0.1719 0.0535 0.0534 0.1225 0.2498 0.3484 0.7502 0.5100 0.0884 0.6609 0.3672 0.5852 0.8440
iter 4: 0.0054 0.0051 0.6928 0.1979 0.5598 0.3732 0.4771 0.4349 0.0506 0.5691 0.0189 0.0085 0.2891 0.7456 0.0785 0.0395 0.0737 0.1210 0.1353 0.0335 0.2836 0.0117 0.0566 0.0778 0.0743 0.1055 0.2131 0.2964 0.0697 0.0912 0.0396 0.0395 0.1611 0.0531 0.0597 0.1258 0.2600 0.3560 0.8062 0.5032 0.0973 0.6739 0.3698 0.5875 0.8485
iter 5: 0.0052 0.0055 0.8355 0.1965 0.5664 0.3710 0.4743 0.4604 0.0520 0.5598 0.0193 0.0091 0.2852 0.7474 0.0800 0.0405 0.0722 0.1213 0.1366 0.0344 0.2788 0.0118 0.0555 0.0756 0.0746 0.0986 0.2190 0.2765 0.0695 0.0932 0.0390 0.0425 0.1650 0.0509 0.0576 0.1305 0.2556 0.3509 0.7738 0.5051 0.0969 0.6902 0.3640 0.6007 0.8326
missRanger object. Extract imputed data via $data
- best iteration: 4
- best average OOB imputation error: 0.2482278
Code
data_train_qb <- seasonalData_lag_qb_train_imp$data
data_train_qb$fantasyPointsMC_lag <- scale(data_train_qb$fantasyPoints_lag, scale = FALSE) # mean-centered
data_train_qb_matrix <- data_train_qb %>%
mutate(across(where(is.factor), ~ as.numeric(as.integer(.)))) %>%
as.matrix()
seasonalData_lag_qb_test_imp <- predict(
object = seasonalData_lag_qb_train_imp,
newdata = seasonalData_lag_qb_test,
seed = 52242)
data_test_qb <- seasonalData_lag_qb_test_imp
data_test_qb_matrix <- data_test_qb %>%
mutate(across(where(is.factor), ~ as.numeric(as.integer(.)))) %>%
as.matrix()Code
Variables to impute: games, ageCentered20, ageCentered20Quadratic, fantasy_points, fantasy_points_ppr, fantasyPoints, carries, rushing_yards, rushing_tds, rushing_fumbles, rushing_fumbles_lost, rushing_first_downs, rushing_2pt_conversions, receptions, targets, receiving_yards, receiving_tds, receiving_fumbles, receiving_fumbles_lost, receiving_air_yards, receiving_yards_after_catch, receiving_first_downs, receiving_2pt_conversions, special_teams_tds, years_of_experience, rushing_epa, air_yards_share, receiving_epa, racr, target_share, wopr, fantasyPoints_lag, rookie_year, draft_number, gs, att.rush, yds.rush, td.rush, x1d.rush, ybc.rush, yac.rush, brk_tkl.rush, att_br.rush, tgt.rec, rec.rec, yds.rec, td.rec, x1d.rec, ybc.rec, yac.rec, brk_tkl.rec, drop.rec, int.rec, ybc_att.rush, yac_att.rush, adot.rec, rat.rec, drop_percent.rec, rec_br.rec, ybc_r.rec, yac_r.rec
Variables used to impute: gsis_id, season, games, gs, years_of_experience, age, ageCentered20, ageCentered20Quadratic, height, weight, rookie_year, draft_number, fantasy_points, fantasy_points_ppr, fantasyPoints, fantasyPoints_lag, carries, rushing_yards, rushing_tds, rushing_fumbles, rushing_fumbles_lost, rushing_first_downs, rushing_epa, rushing_2pt_conversions, receptions, targets, receiving_yards, receiving_tds, receiving_fumbles, receiving_fumbles_lost, receiving_air_yards, receiving_yards_after_catch, receiving_first_downs, receiving_epa, receiving_2pt_conversions, racr, target_share, air_yards_share, wopr, special_teams_tds, ybc_att.rush, yac_att.rush, att.rush, yds.rush, td.rush, x1d.rush, ybc.rush, yac.rush, brk_tkl.rush, att_br.rush, ybc_r.rec, yac_r.rec, adot.rec, rat.rec, tgt.rec, rec.rec, yds.rec, td.rec, x1d.rec, ybc.rec, yac.rec, brk_tkl.rec, drop.rec, int.rec, drop_percent.rec, rec_br.rec
games agCn20 agC20Q fntsy_ fnts__ fntsyP carris rshng_y rshng_t rshng_f rshng_fm_ rshng_fr_ rsh_2_ rcptns targts rcvng_y rcvng_t rcvng_f rcvng_fm_ rcvng_r_ rcv___ rcvng_fr_ rcv_2_ spcl__ yrs_f_ rshng_p ar_yr_ rcvng_p racr trgt_s wopr fntsP_ rok_yr drft_n gs att.rs yds.rs td.rsh x1d.rs ybc.rs yc.rsh brk_tkl.rs att_b. tgt.rc rec.rc yds.rc td.rec x1d.rc ybc.rc yac.rc brk_tkl.rc drp.rc int.rc ybc_t. yc_tt. adt.rc rat.rc drp_p. rc_br. ybc_r. yc_r.r
iter 1: 0.8865 0.0057 0.0031 0.4544 0.0178 0.0032 0.0745 0.0233 0.1462 0.4895 0.2594 0.0295 0.9849 0.0690 0.0666 0.0534 0.4327 0.8626 0.4824 0.6841 0.0322 0.0614 1.0171 0.8263 0.1817 0.4512 0.3321 0.3894 0.5211 0.4549 0.1817 0.5440 0.0197 0.5999 0.1700 0.0244 0.0222 0.0792 0.0297 0.0527 0.0520 0.2134 0.3431 0.0252 0.0180 0.0257 0.1634 0.0437 0.3108 0.0217 0.3925 0.4610 0.6941 0.4880 0.5402 0.2670 0.2026 0.3482 0.1596 0.2698 0.3637
iter 2: 0.2755 0.0162 0.0207 0.0063 0.0037 0.0044 0.0161 0.0148 0.0912 0.2524 0.2898 0.0248 0.9832 0.0273 0.0444 0.0233 0.2065 0.4600 0.4891 0.1285 0.0332 0.0457 1.0175 0.8566 0.1824 0.4212 0.2329 0.3099 0.5605 0.2569 0.1742 0.5373 0.0424 0.6377 0.1653 0.0167 0.0123 0.0859 0.0302 0.0367 0.0349 0.1030 0.3689 0.0144 0.0159 0.0195 0.1403 0.0434 0.1549 0.0190 0.3840 0.1050 0.5453 0.4882 0.5616 0.2472 0.1953 0.1525 0.1687 0.2595 0.3619
iter 3: 0.2744 0.0163 0.0231 0.0062 0.0038 0.0047 0.0152 0.0137 0.0980 0.2601 0.2906 0.0244 0.9800 0.0265 0.0347 0.0231 0.2101 0.4638 0.4954 0.1284 0.0283 0.0458 1.0114 0.8731 0.1818 0.4117 0.2278 0.3037 0.5699 0.2052 0.1800 0.5389 0.0400 0.6423 0.1624 0.0166 0.0124 0.0893 0.0306 0.0374 0.0356 0.1074 0.3628 0.0144 0.0163 0.0187 0.1390 0.0463 0.1583 0.0190 0.3882 0.1062 0.5642 0.4796 0.5570 0.2380 0.1935 0.1586 0.1588 0.2625 0.3648
iter 4: 0.2776 0.0169 0.0220 0.0063 0.0038 0.0045 0.0151 0.0138 0.0979 0.2584 0.2846 0.0243 0.9782 0.0263 0.0281 0.0221 0.1968 0.4594 0.4817 0.1267 0.0290 0.0462 1.0104 0.8614 0.1854 0.4216 0.2333 0.3004 0.5467 0.1917 0.1815 0.5353 0.0443 0.6503 0.1657 0.0166 0.0121 0.0905 0.0313 0.0378 0.0357 0.1041 0.3437 0.0155 0.0159 0.0185 0.1405 0.0441 0.1613 0.0196 0.3816 0.1117 0.5682 0.5011 0.5585 0.2421 0.1975 0.1520 0.1770 0.2650 0.3647
iter 5: 0.2752 0.0163 0.0226 0.0063 0.0038 0.0045 0.0158 0.0138 0.1015 0.2614 0.2857 0.0242 0.9740 0.0250 0.0303 0.0218 0.2004 0.4607 0.4810 0.1167 0.0285 0.0449 1.0077 0.8658 0.1835 0.4182 0.2170 0.2995 0.5690 0.2010 0.1794 0.5375 0.0385 0.6487 0.1652 0.0166 0.0124 0.0878 0.0306 0.0368 0.0353 0.1069 0.3539 0.0154 0.0159 0.0193 0.1409 0.0447 0.1598 0.0205 0.3873 0.1062 0.5583 0.4895 0.5501 0.2418 0.1979 0.1713 0.1726 0.2625 0.3596
iter 6: 0.2760 0.0158 0.0223 0.0063 0.0037 0.0046 0.0150 0.0144 0.0982 0.2568 0.2816 0.0238 0.9810 0.0253 0.0273 0.0223 0.2141 0.4606 0.4881 0.1386 0.0300 0.0457 1.0174 0.8605 0.1821 0.4188 0.2263 0.2985 0.5497 0.1779 0.1536 0.5388 0.0389 0.6422 0.1668 0.0162 0.0119 0.0897 0.0305 0.0376 0.0356 0.1066 0.3529 0.0149 0.0159 0.0196 0.1446 0.0450 0.1585 0.0197 0.3857 0.1001 0.5607 0.4948 0.5478 0.2487 0.1945 0.1438 0.1543 0.2568 0.3612
iter 7: 0.2748 0.0158 0.0212 0.0064 0.0039 0.0047 0.0149 0.0141 0.0986 0.2611 0.2877 0.0241 0.9755 0.0253 0.0310 0.0223 0.2163 0.4553 0.4885 0.1335 0.0293 0.0456 1.0096 0.8575 0.1821 0.4236 0.2203 0.2998 0.5510 0.2107 0.1797 0.5354 0.0416 0.6395 0.1646 0.0166 0.0117 0.0895 0.0310 0.0371 0.0361 0.1073 0.3547 0.0154 0.0156 0.0193 0.1410 0.0449 0.1628 0.0201 0.3892 0.1076 0.5609 0.4946 0.5643 0.2392 0.1899 0.1540 0.1423 0.2667 0.3603
missRanger object. Extract imputed data via $data
- best iteration: 6
- best average OOB imputation error: 0.2175486
Code
data_all_rb <- seasonalData_lag_rb_all_imp$data
data_all_rb$fantasyPointsMC_lag <- scale(data_all_rb$fantasyPoints_lag, scale = FALSE) # mean-centered
data_all_rb_matrix <- data_all_rb %>%
mutate(across(where(is.factor), ~ as.numeric(as.integer(.)))) %>%
as.matrix()
newData_rb <- data_all_rb %>%
filter(season == max(season, na.rm = TRUE)) %>%
select(-fantasyPoints_lag, -fantasyPointsMC_lag)
newData_rb_matrix <- data_all_rb_matrix[
data_all_rb_matrix[, "season"] == max(data_all_rb_matrix[, "season"], na.rm = TRUE), # keep only rows with the most recent season
, # all columns
drop = FALSE]
dropCol_rb <- which(colnames(newData_rb_matrix) %in% c("fantasyPoints_lag","fantasyPointsMC_lag"))
newData_rb_matrix <- newData_rb_matrix[, -dropCol_rb, drop = FALSE]
seasonalData_lag_rb_train_imp <- missRanger::missRanger(
seasonalData_lag_rb_train,
pmm.k = 5,
verbose = 2,
seed = 52242,
keep_forests = TRUE)
Variables to impute: games, ageCentered20, ageCentered20Quadratic, fantasy_points, fantasy_points_ppr, fantasyPoints, carries, rushing_yards, rushing_tds, rushing_fumbles, rushing_fumbles_lost, rushing_first_downs, rushing_2pt_conversions, receptions, targets, receiving_yards, receiving_tds, receiving_fumbles, receiving_fumbles_lost, receiving_air_yards, receiving_yards_after_catch, receiving_first_downs, receiving_2pt_conversions, special_teams_tds, years_of_experience, rushing_epa, air_yards_share, receiving_epa, racr, target_share, wopr, fantasyPoints_lag, rookie_year, draft_number, gs, att.rush, yds.rush, td.rush, x1d.rush, ybc.rush, yac.rush, brk_tkl.rush, att_br.rush, tgt.rec, rec.rec, yds.rec, td.rec, x1d.rec, ybc.rec, yac.rec, brk_tkl.rec, drop.rec, int.rec, ybc_att.rush, yac_att.rush, adot.rec, rat.rec, drop_percent.rec, rec_br.rec, ybc_r.rec, yac_r.rec
Variables used to impute: gsis_id, season, games, gs, years_of_experience, age, ageCentered20, ageCentered20Quadratic, height, weight, rookie_year, draft_number, fantasy_points, fantasy_points_ppr, fantasyPoints, fantasyPoints_lag, carries, rushing_yards, rushing_tds, rushing_fumbles, rushing_fumbles_lost, rushing_first_downs, rushing_epa, rushing_2pt_conversions, receptions, targets, receiving_yards, receiving_tds, receiving_fumbles, receiving_fumbles_lost, receiving_air_yards, receiving_yards_after_catch, receiving_first_downs, receiving_epa, receiving_2pt_conversions, racr, target_share, air_yards_share, wopr, special_teams_tds, ybc_att.rush, yac_att.rush, att.rush, yds.rush, td.rush, x1d.rush, ybc.rush, yac.rush, brk_tkl.rush, att_br.rush, ybc_r.rec, yac_r.rec, adot.rec, rat.rec, tgt.rec, rec.rec, yds.rec, td.rec, x1d.rec, ybc.rec, yac.rec, brk_tkl.rec, drop.rec, int.rec, drop_percent.rec, rec_br.rec
games agCn20 agC20Q fntsy_ fnts__ fntsyP carris rshng_y rshng_t rshng_f rshng_fm_ rshng_fr_ rsh_2_ rcptns targts rcvng_y rcvng_t rcvng_f rcvng_fm_ rcvng_r_ rcv___ rcvng_fr_ rcv_2_ spcl__ yrs_f_ rshng_p ar_yr_ rcvng_p racr trgt_s wopr fntsP_ rok_yr drft_n gs att.rs yds.rs td.rsh x1d.rs ybc.rs yc.rsh brk_tkl.rs att_b. tgt.rc rec.rc yds.rc td.rec x1d.rc ybc.rc yac.rc brk_tkl.rc drp.rc int.rc ybc_t. yc_tt. adt.rc rat.rc drp_p. rc_br. ybc_r. yc_r.r
iter 1: 0.8759 0.0072 0.0036 0.4578 0.0178 0.0035 0.0736 0.0229 0.1524 0.4776 0.2679 0.0288 0.9965 0.0749 0.0744 0.0553 0.4578 0.8604 0.4998 0.6821 0.0360 0.0639 1.0042 0.8380 0.1806 0.4662 0.3419 0.3961 0.5595 0.4715 0.1968 0.5338 0.0246 0.5882 0.1726 0.0265 0.0235 0.0849 0.0311 0.0550 0.0521 0.2131 0.3689 0.0281 0.0197 0.0286 0.1742 0.0463 0.3114 0.0229 0.3942 0.4806 0.7239 0.5199 0.5631 0.2865 0.2195 0.3630 0.2052 0.2596 0.4091
iter 2: 0.2745 0.0177 0.0266 0.0067 0.0041 0.0049 0.0169 0.0154 0.1017 0.2590 0.2956 0.0237 0.9814 0.0286 0.0522 0.0240 0.2187 0.4582 0.4919 0.1541 0.0362 0.0475 1.0075 0.8811 0.1822 0.4481 0.2377 0.3184 0.6116 0.2628 0.2007 0.5254 0.0473 0.6411 0.1653 0.0179 0.0132 0.0940 0.0325 0.0392 0.0375 0.1057 0.3678 0.0161 0.0169 0.0196 0.1510 0.0484 0.1521 0.0202 0.3941 0.1035 0.5567 0.5120 0.5666 0.2466 0.2087 0.1733 0.1699 0.2524 0.4066
iter 3: 0.2766 0.0190 0.0273 0.0067 0.0041 0.0048 0.0159 0.0149 0.0971 0.2615 0.2952 0.0245 0.9668 0.0278 0.0409 0.0240 0.2180 0.4648 0.4931 0.1319 0.0350 0.0495 1.0128 0.8907 0.1820 0.4366 0.2459 0.3124 0.6236 0.2555 0.2114 0.5276 0.0438 0.6314 0.1658 0.0175 0.0122 0.0899 0.0319 0.0386 0.0386 0.1100 0.3783 0.0155 0.0165 0.0194 0.1477 0.0474 0.1499 0.0194 0.3929 0.1121 0.5761 0.5245 0.5651 0.2490 0.2103 0.1767 0.1817 0.2658 0.4106
missRanger object. Extract imputed data via $data
- best iteration: 2
- best average OOB imputation error: 0.226086
Code
data_train_rb <- seasonalData_lag_rb_train_imp$data
data_train_rb$fantasyPointsMC_lag <- scale(data_train_rb$fantasyPoints_lag, scale = FALSE) # mean-centered
data_train_rb_matrix <- data_train_rb %>%
mutate(across(where(is.factor), ~ as.numeric(as.integer(.)))) %>%
as.matrix()
seasonalData_lag_rb_test_imp <- predict(
object = seasonalData_lag_rb_train_imp,
newdata = seasonalData_lag_rb_test,
seed = 52242)
data_test_rb <- seasonalData_lag_rb_test_imp
data_test_rb_matrix <- data_test_rb %>%
mutate(across(where(is.factor), ~ as.numeric(as.integer(.)))) %>%
as.matrix()Code
Variables to impute: fantasy_points, fantasy_points_ppr, special_teams_tds, years_of_experience, receiving_epa, racr, air_yards_share, target_share, wopr, fantasyPoints_lag, rookie_year, rushing_epa, draft_number, gs, att.rush, yds.rush, td.rush, x1d.rush, ybc.rush, yac.rush, brk_tkl.rush, att_br.rush, tgt.rec, rec.rec, yds.rec, td.rec, x1d.rec, ybc.rec, yac.rec, brk_tkl.rec, drop.rec, int.rec, adot.rec, rat.rec, drop_percent.rec, rec_br.rec, ybc_r.rec, yac_r.rec, ybc_att.rush, yac_att.rush
Variables used to impute: gsis_id, season, games, gs, years_of_experience, age, ageCentered20, ageCentered20Quadratic, height, weight, rookie_year, draft_number, fantasy_points, fantasy_points_ppr, fantasyPoints, fantasyPoints_lag, carries, rushing_yards, rushing_tds, rushing_fumbles, rushing_fumbles_lost, rushing_first_downs, rushing_epa, rushing_2pt_conversions, receptions, targets, receiving_yards, receiving_tds, receiving_fumbles, receiving_fumbles_lost, receiving_air_yards, receiving_yards_after_catch, receiving_first_downs, receiving_epa, receiving_2pt_conversions, racr, target_share, air_yards_share, wopr, special_teams_tds, ybc_att.rush, yac_att.rush, att.rush, yds.rush, td.rush, x1d.rush, ybc.rush, yac.rush, brk_tkl.rush, att_br.rush, ybc_r.rec, yac_r.rec, adot.rec, rat.rec, tgt.rec, rec.rec, yds.rec, td.rec, x1d.rec, ybc.rec, yac.rec, brk_tkl.rec, drop.rec, int.rec, drop_percent.rec, rec_br.rec
fntsy_ fnts__ spcl__ yrs_f_ rcvng_ racr ar_yr_ trgt_s wopr fntsP_ rok_yr rshng_ drft_n gs att.rs yds.rs td.rsh x1d.rs ybc.rs yc.rsh brk_tkl.rs att_b. tgt.rc rec.rc yds.rc td.rec x1d.rc ybc.rc yac.rc brk_tkl.rc drp.rc int.rc adt.rc rat.rc drp_p. rc_br. ybc_r. yc_r.r ybc_t. yc_tt.
iter 1: 0.0061 0.0010 0.7104 0.1566 0.1040 0.8131 0.1013 0.1722 0.0402 0.4890 0.0150 0.3811 0.6654 0.1459 0.1184 0.0898 0.2353 0.1234 0.0966 0.2670 0.6383 0.3084 0.0198 0.0136 0.0151 0.0671 0.0135 0.0268 0.0442 0.4465 0.4320 0.4674 0.2961 0.1410 0.3819 0.1840 0.2251 0.3929 0.2568 0.4760
iter 2: 0.0058 0.0019 0.7826 0.1601 0.0835 0.7518 0.0607 0.0930 0.0452 0.4939 0.0296 0.3301 0.6843 0.1440 0.0851 0.0600 0.2638 0.1161 0.0708 0.1804 0.3103 0.3223 0.0109 0.0108 0.0096 0.0719 0.0139 0.0200 0.0318 0.4476 0.0778 0.3692 0.2401 0.1448 0.1629 0.1601 0.2261 0.3793 0.2536 0.4775
iter 3: 0.0061 0.0019 0.7857 0.1593 0.0829 0.7421 0.0580 0.0986 0.0481 0.4946 0.0318 0.3334 0.6890 0.1430 0.0823 0.0604 0.2595 0.1177 0.0728 0.1802 0.3077 0.3194 0.0109 0.0114 0.0095 0.0724 0.0133 0.0199 0.0312 0.4411 0.0767 0.3687 0.2369 0.1455 0.1530 0.1660 0.2169 0.3878 0.2466 0.4716
iter 4: 0.0060 0.0018 0.7874 0.1604 0.0832 0.7394 0.0591 0.0940 0.0479 0.4926 0.0301 0.3317 0.6896 0.1434 0.0863 0.0601 0.2562 0.1227 0.0711 0.1900 0.3089 0.3194 0.0105 0.0112 0.0095 0.0707 0.0140 0.0202 0.0318 0.4447 0.0784 0.3674 0.2339 0.1423 0.1592 0.1700 0.2254 0.3886 0.2552 0.4662
missRanger object. Extract imputed data via $data
- best iteration: 3
- best average OOB imputation error: 0.203846
Code
data_all_wr <- seasonalData_lag_wr_all_imp$data
data_all_wr$fantasyPointsMC_lag <- scale(data_all_wr$fantasyPoints_lag, scale = FALSE) # mean-centered
data_all_wr_matrix <- data_all_wr %>%
mutate(across(where(is.factor), ~ as.numeric(as.integer(.)))) %>%
as.matrix()
newData_wr <- data_all_wr %>%
filter(season == max(season, na.rm = TRUE)) %>%
select(-fantasyPoints_lag, -fantasyPointsMC_lag)
newData_wr_matrix <- data_all_wr_matrix[
data_all_wr_matrix[, "season"] == max(data_all_wr_matrix[, "season"], na.rm = TRUE), # keep only rows with the most recent season
, # all columns
drop = FALSE]
dropCol_wr <- which(colnames(newData_wr_matrix) %in% c("fantasyPoints_lag","fantasyPointsMC_lag"))
newData_wr_matrix <- newData_wr_matrix[, -dropCol_wr, drop = FALSE]
seasonalData_lag_wr_train_imp <- missRanger::missRanger(
seasonalData_lag_wr_train,
pmm.k = 5,
verbose = 2,
seed = 52242,
keep_forests = TRUE)
Variables to impute: fantasy_points, fantasy_points_ppr, special_teams_tds, years_of_experience, receiving_epa, racr, air_yards_share, target_share, wopr, fantasyPoints_lag, rookie_year, rushing_epa, draft_number, gs, att.rush, yds.rush, td.rush, x1d.rush, ybc.rush, yac.rush, brk_tkl.rush, att_br.rush, tgt.rec, rec.rec, yds.rec, td.rec, x1d.rec, ybc.rec, yac.rec, brk_tkl.rec, drop.rec, int.rec, adot.rec, rat.rec, drop_percent.rec, rec_br.rec, ybc_r.rec, yac_r.rec, ybc_att.rush, yac_att.rush
Variables used to impute: gsis_id, season, games, gs, years_of_experience, age, ageCentered20, ageCentered20Quadratic, height, weight, rookie_year, draft_number, fantasy_points, fantasy_points_ppr, fantasyPoints, fantasyPoints_lag, carries, rushing_yards, rushing_tds, rushing_fumbles, rushing_fumbles_lost, rushing_first_downs, rushing_epa, rushing_2pt_conversions, receptions, targets, receiving_yards, receiving_tds, receiving_fumbles, receiving_fumbles_lost, receiving_air_yards, receiving_yards_after_catch, receiving_first_downs, receiving_epa, receiving_2pt_conversions, racr, target_share, air_yards_share, wopr, special_teams_tds, ybc_att.rush, yac_att.rush, att.rush, yds.rush, td.rush, x1d.rush, ybc.rush, yac.rush, brk_tkl.rush, att_br.rush, ybc_r.rec, yac_r.rec, adot.rec, rat.rec, tgt.rec, rec.rec, yds.rec, td.rec, x1d.rec, ybc.rec, yac.rec, brk_tkl.rec, drop.rec, int.rec, drop_percent.rec, rec_br.rec
fntsy_ fnts__ spcl__ yrs_f_ rcvng_ racr ar_yr_ trgt_s wopr fntsP_ rok_yr rshng_ drft_n gs att.rs yds.rs td.rsh x1d.rs ybc.rs yc.rsh brk_tkl.rs att_b. tgt.rc rec.rc yds.rc td.rec x1d.rc ybc.rc yac.rc brk_tkl.rc drp.rc int.rc adt.rc rat.rc drp_p. rc_br. ybc_r. yc_r.r ybc_t. yc_tt.
iter 1: 0.0064 0.0010 0.7029 0.1611 0.1089 0.8443 0.1021 0.1643 0.0427 0.4935 0.0173 0.3461 0.6788 0.1427 0.1364 0.0993 0.2403 0.1243 0.0979 0.2745 0.6190 0.3171 0.0201 0.0147 0.0159 0.0734 0.0140 0.0280 0.0454 0.4502 0.4439 0.4733 0.3088 0.1641 0.4547 0.2192 0.2439 0.4227 0.2921 0.5068
iter 2: 0.0063 0.0020 0.7835 0.1630 0.0901 0.8044 0.0674 0.0936 0.0479 0.4930 0.0331 0.3235 0.7090 0.1417 0.0896 0.0659 0.2659 0.1273 0.0752 0.1920 0.3068 0.3225 0.0112 0.0116 0.0101 0.0753 0.0141 0.0210 0.0333 0.4431 0.0809 0.3676 0.2571 0.1617 0.1735 0.1797 0.2441 0.3996 0.2911 0.4923
iter 3: 0.0063 0.0020 0.7710 0.1639 0.0881 0.7954 0.0646 0.0982 0.0515 0.4956 0.0338 0.3200 0.7088 0.1413 0.0900 0.0640 0.2565 0.1250 0.0735 0.1989 0.3082 0.3280 0.0114 0.0119 0.0096 0.0763 0.0141 0.0216 0.0326 0.4388 0.0807 0.3703 0.2582 0.1623 0.1657 0.2018 0.2375 0.4016 0.2838 0.4794
iter 4: 0.0062 0.0020 0.7792 0.1625 0.0877 0.8043 0.0632 0.0919 0.0477 0.4963 0.0341 0.3239 0.7038 0.1420 0.0950 0.0653 0.2664 0.1309 0.0767 0.2025 0.2933 0.3076 0.0109 0.0119 0.0097 0.0745 0.0143 0.0217 0.0326 0.4432 0.0804 0.3688 0.2584 0.1605 0.1931 0.2013 0.2378 0.4119 0.2824 0.4860
missRanger object. Extract imputed data via $data
- best iteration: 3
- best average OOB imputation error: 0.2110456
Code
data_train_wr <- seasonalData_lag_wr_train_imp$data
data_train_wr$fantasyPointsMC_lag <- scale(data_train_wr$fantasyPoints_lag, scale = FALSE) # mean-centered
data_train_wr_matrix <- data_train_wr %>%
mutate(across(where(is.factor), ~ as.numeric(as.integer(.)))) %>%
as.matrix()
seasonalData_lag_wr_test_imp <- predict(
object = seasonalData_lag_wr_train_imp,
newdata = seasonalData_lag_wr_test,
seed = 52242)
data_test_wr <- seasonalData_lag_wr_test_imp
data_test_wr_matrix <- data_test_wr %>%
mutate(across(where(is.factor), ~ as.numeric(as.integer(.)))) %>%
as.matrix()Code
Variables to impute: games, ageCentered20, ageCentered20Quadratic, fantasy_points, fantasy_points_ppr, fantasyPoints, carries, rushing_yards, rushing_tds, rushing_fumbles, rushing_fumbles_lost, rushing_first_downs, rushing_2pt_conversions, receptions, targets, receiving_yards, receiving_tds, receiving_fumbles, receiving_fumbles_lost, receiving_air_yards, receiving_yards_after_catch, receiving_first_downs, receiving_2pt_conversions, special_teams_tds, years_of_experience, receiving_epa, racr, air_yards_share, target_share, wopr, fantasyPoints_lag, rookie_year, draft_number, gs, att.rush, yds.rush, td.rush, x1d.rush, ybc.rush, yac.rush, brk_tkl.rush, att_br.rush, tgt.rec, rec.rec, yds.rec, td.rec, x1d.rec, ybc.rec, yac.rec, brk_tkl.rec, drop.rec, int.rec, adot.rec, rat.rec, drop_percent.rec, rec_br.rec, ybc_r.rec, yac_r.rec, rushing_epa, ybc_att.rush, yac_att.rush
Variables used to impute: gsis_id, season, games, gs, years_of_experience, age, ageCentered20, ageCentered20Quadratic, height, weight, rookie_year, draft_number, fantasy_points, fantasy_points_ppr, fantasyPoints, fantasyPoints_lag, carries, rushing_yards, rushing_tds, rushing_fumbles, rushing_fumbles_lost, rushing_first_downs, rushing_epa, rushing_2pt_conversions, receptions, targets, receiving_yards, receiving_tds, receiving_fumbles, receiving_fumbles_lost, receiving_air_yards, receiving_yards_after_catch, receiving_first_downs, receiving_epa, receiving_2pt_conversions, racr, target_share, air_yards_share, wopr, special_teams_tds, ybc_att.rush, yac_att.rush, att.rush, yds.rush, td.rush, x1d.rush, ybc.rush, yac.rush, brk_tkl.rush, att_br.rush, ybc_r.rec, yac_r.rec, adot.rec, rat.rec, tgt.rec, rec.rec, yds.rec, td.rec, x1d.rec, ybc.rec, yac.rec, brk_tkl.rec, drop.rec, int.rec, drop_percent.rec, rec_br.rec
games agCn20 agC20Q fntsy_ fnts__ fntsyP carris rshng_y rshng_t rshng_f rshng_fm_ rshng_fr_ rsh_2_ rcptns targts rcvng_y rcvng_t rcvng_f rcvng_fm_ rcvng_r_ rcv___ rcvng_fr_ rcv_2_ spcl__ yrs_f_ rcvng_p racr ar_yr_ trgt_s wopr fntsP_ rok_yr drft_n gs att.rs yds.rs td.rsh x1d.rs ybc.rs yc.rsh brk_tkl.rs att_b. tgt.rc rec.rc yds.rc td.rec x1d.rc ybc.rc yac.rc brk_tkl.rc drp.rc int.rc adt.rc rat.rc drp_p. rc_br. ybc_r. yc_r.r rshng_p ybc_t. yc_tt.
iter 1: 0.8157 0.0061 0.0030 0.3406 0.0194 0.0039 0.5253 0.2259 0.2452 0.7083 0.6874 0.0802 1.1303 0.0281 0.0558 0.0255 0.0845 0.8134 0.4317 0.0655 0.0784 0.0253 0.9716 1.0271 0.1530 0.1689 0.6899 0.1092 0.4432 0.1004 0.4764 0.0180 0.6054 0.3846 0.0762 0.0832 0.1564 0.0618 0.0704 0.2123 0.3921 0.6733 0.0290 0.0207 0.0226 0.1012 0.0212 0.0420 0.0603 0.4332 0.4640 0.4996 0.2804 0.1667 0.3542 0.1652 0.2843 0.3948 0.3270 0.6620 0.7439
iter 2: 0.1712 0.0175 0.0256 0.0106 0.0037 0.0055 0.1140 0.1113 0.0990 0.5369 0.7422 0.0852 1.1286 0.0193 0.0200 0.0128 0.0862 0.4248 0.4659 0.0206 0.0529 0.0217 0.9711 1.0114 0.1561 0.1397 0.6715 0.0766 0.1819 0.1085 0.4649 0.0366 0.6346 0.3880 0.0722 0.0728 0.1592 0.0680 0.0759 0.2034 0.3651 0.6811 0.0164 0.0158 0.0161 0.1080 0.0211 0.0327 0.0475 0.4342 0.1149 0.4173 0.2589 0.1742 0.1467 0.1531 0.2941 0.3851 0.3357 0.6846 0.7397
iter 3: 0.1689 0.0170 0.0261 0.0114 0.0040 0.0056 0.1190 0.1155 0.0978 0.6088 0.7899 0.0945 1.1731 0.0195 0.0203 0.0132 0.0964 0.4270 0.4608 0.0202 0.0525 0.0214 0.9694 1.0265 0.1560 0.1380 0.6453 0.0751 0.1794 0.1204 0.4642 0.0364 0.6369 0.3853 0.0779 0.0786 0.1497 0.0569 0.0932 0.2027 0.4003 0.6633 0.0171 0.0164 0.0167 0.1049 0.0220 0.0335 0.0466 0.4371 0.1141 0.4304 0.2665 0.1775 0.1464 0.1537 0.2916 0.3720 0.3137 0.6640 0.7770
missRanger object. Extract imputed data via $data
- best iteration: 2
- best average OOB imputation error: 0.2477098
Code
data_all_te <- seasonalData_lag_te_all_imp$data
data_all_te$fantasyPointsMC_lag <- scale(data_all_te$fantasyPoints_lag, scale = FALSE) # mean-centered
data_all_te_matrix <- data_all_te %>%
mutate(across(where(is.factor), ~ as.numeric(as.integer(.)))) %>%
as.matrix()
newData_te <- data_all_te %>%
filter(season == max(season, na.rm = TRUE)) %>%
select(-fantasyPoints_lag, -fantasyPointsMC_lag)
newData_te_matrix <- data_all_te_matrix[
data_all_te_matrix[, "season"] == max(data_all_te_matrix[, "season"], na.rm = TRUE), # keep only rows with the most recent season
, # all columns
drop = FALSE]
dropCol_te <- which(colnames(newData_te_matrix) %in% c("fantasyPoints_lag","fantasyPointsMC_lag"))
newData_te_matrix <- newData_te_matrix[, -dropCol_te, drop = FALSE]
seasonalData_lag_te_train_imp <- missRanger::missRanger(
seasonalData_lag_te_train,
pmm.k = 5,
verbose = 2,
seed = 52242,
keep_forests = TRUE)
Variables to impute: games, years_of_experience, ageCentered20, ageCentered20Quadratic, fantasy_points, fantasy_points_ppr, fantasyPoints, carries, rushing_yards, rushing_tds, rushing_fumbles, rushing_fumbles_lost, rushing_first_downs, rushing_2pt_conversions, receptions, targets, receiving_yards, receiving_tds, receiving_fumbles, receiving_fumbles_lost, receiving_air_yards, receiving_yards_after_catch, receiving_first_downs, receiving_2pt_conversions, special_teams_tds, receiving_epa, racr, air_yards_share, target_share, wopr, fantasyPoints_lag, rookie_year, draft_number, gs, att.rush, yds.rush, td.rush, x1d.rush, ybc.rush, yac.rush, brk_tkl.rush, att_br.rush, tgt.rec, rec.rec, yds.rec, td.rec, x1d.rec, ybc.rec, yac.rec, brk_tkl.rec, drop.rec, int.rec, adot.rec, rat.rec, drop_percent.rec, rec_br.rec, ybc_r.rec, yac_r.rec, rushing_epa, ybc_att.rush, yac_att.rush
Variables used to impute: gsis_id, season, games, gs, years_of_experience, age, ageCentered20, ageCentered20Quadratic, height, weight, rookie_year, draft_number, fantasy_points, fantasy_points_ppr, fantasyPoints, fantasyPoints_lag, carries, rushing_yards, rushing_tds, rushing_fumbles, rushing_fumbles_lost, rushing_first_downs, rushing_epa, rushing_2pt_conversions, receptions, targets, receiving_yards, receiving_tds, receiving_fumbles, receiving_fumbles_lost, receiving_air_yards, receiving_yards_after_catch, receiving_first_downs, receiving_epa, receiving_2pt_conversions, racr, target_share, air_yards_share, wopr, special_teams_tds, ybc_att.rush, yac_att.rush, att.rush, yds.rush, td.rush, x1d.rush, ybc.rush, yac.rush, brk_tkl.rush, att_br.rush, ybc_r.rec, yac_r.rec, adot.rec, rat.rec, tgt.rec, rec.rec, yds.rec, td.rec, x1d.rec, ybc.rec, yac.rec, brk_tkl.rec, drop.rec, int.rec, drop_percent.rec, rec_br.rec
games yrs_f_ agCn20 agC20Q fntsy_ fnts__ fntsyP carris rshng_y rshng_t rshng_f rshng_fm_ rshng_fr_ rsh_2_ rcptns targts rcvng_y rcvng_t rcvng_f rcvng_fm_ rcvng_r_ rcv___ rcvng_fr_ rcv_2_ spcl__ rcvng_p racr ar_yr_ trgt_s wopr fntsP_ rok_yr drft_n gs att.rs yds.rs td.rsh x1d.rs ybc.rs yc.rsh brk_tkl.rs att_b. tgt.rc rec.rc yds.rc td.rec x1d.rc ybc.rc yac.rc brk_tkl.rc drp.rc int.rc adt.rc rat.rc drp_p. rc_br. ybc_r. yc_r.r rshng_p ybc_t. yc_tt.
iter 1: 0.8094 0.1093 0.0070 0.0035 0.3272 0.0235 0.0052 0.2840 0.1426 0.2634 0.8628 0.7885 0.0924 1.1067 0.0298 0.0611 0.0249 0.0969 0.8177 0.4537 0.0650 0.0804 0.0249 0.9680 1.0235 0.1738 0.5438 0.0868 0.4123 0.1172 0.4597 0.0189 0.6057 0.3973 0.0877 0.0886 0.1516 0.0467 0.0593 0.2086 0.4018 0.6464 0.0296 0.0223 0.0237 0.1062 0.0207 0.0428 0.0579 0.4367 0.4700 0.4818 0.3045 0.1724 0.4722 0.2410 0.2693 0.4025 0.3943 0.4791 0.7521
iter 2: 0.1728 0.1469 0.0179 0.0289 0.0104 0.0039 0.0051 0.0863 0.0763 0.1528 0.7880 0.9474 0.0849 1.0234 0.0193 0.0198 0.0137 0.0915 0.4327 0.4835 0.0238 0.0558 0.0221 0.9617 1.0376 0.1464 0.5141 0.0630 0.1827 0.1062 0.4562 0.0379 0.6361 0.3908 0.0641 0.0767 0.1425 0.0603 0.0747 0.1970 0.3903 0.6647 0.0182 0.0171 0.0165 0.1074 0.0226 0.0332 0.0503 0.4361 0.1170 0.4096 0.2673 0.1862 0.2255 0.2386 0.2793 0.4004 0.3648 0.5070 0.7621
iter 3: 0.1713 0.1447 0.0195 0.0276 0.0104 0.0036 0.0051 0.0796 0.0889 0.1611 0.8505 0.9348 0.0904 1.0447 0.0196 0.0205 0.0134 0.0901 0.4465 0.4867 0.0233 0.0569 0.0222 0.9519 1.0103 0.1457 0.5062 0.0617 0.1698 0.1115 0.4530 0.0382 0.6521 0.3899 0.0665 0.0681 0.1457 0.0647 0.0866 0.2055 0.3919 0.6791 0.0169 0.0169 0.0168 0.1107 0.0213 0.0339 0.0500 0.4315 0.1200 0.4148 0.2745 0.1822 0.1947 0.2205 0.2778 0.4032 0.3639 0.4933 0.7741
missRanger object. Extract imputed data via $data
- best iteration: 2
- best average OOB imputation error: 0.2519559
Code
data_train_te <- seasonalData_lag_te_train_imp$data
data_train_te$fantasyPointsMC_lag <- scale(data_train_te$fantasyPoints_lag, scale = FALSE) # mean-centered
data_train_te_matrix <- data_train_te %>%
mutate(across(where(is.factor), ~ as.numeric(as.integer(.)))) %>%
as.matrix()
seasonalData_lag_te_test_imp <- predict(
object = seasonalData_lag_te_train_imp,
newdata = seasonalData_lag_te_test,
seed = 52242)
data_test_te <- seasonalData_lag_te_test_imp
data_test_te_matrix <- data_test_te %>%
mutate(across(where(is.factor), ~ as.numeric(as.integer(.)))) %>%
as.matrix()19.5 Identify Cores for Parallel Processing
19.6 Fitting the Traditional Regression Models
19.6.1 Regression with One Predictor
19.6.2 Regression with Multiple Predictors
19.7 Fitting the Machine Learning Models
19.7.1 Least Absolute Shrinkage and Selection Option (LASSO)
19.7.2 Ridge Regression
19.7.3 Elastic Net
19.7.4 Random Forest Machine Learning
19.7.4.1 Cross-Sectional Data
We use the caret package (Kuhn, 2024). We use the parallel (R-parallel?) and doParallel (Corporation & Weston, 2022) packages for parallel (faster) processing.
Code
cl <- parallel::makeCluster(num_cores)
doParallel::registerDoParallel(cl)
set.seed(52242)
randomForest_qb <- caret::train(
fantasyPoints_lag ~ ., # use all predictors
data = seasonalData_lag_subsetQB_imp$ximp,
method = "rf",
trControl = trainControl(
method = "cv",
number = 10)) # 10-fold cross-validationError in eval(expr, p): object 'seasonalData_lag_subsetQB_imp' not found
Code
Error in eval(expr, p): object 'seasonalData_lag_subsetRB_imp' not found
Code
Error in eval(expr, p): object 'seasonalData_lag_subsetWR_imp' not found
Code
Error in eval(expr, p): object 'seasonalData_lag_subsetTE_imp' not found
Error: object 'randomForest_qb' not found
Error: object 'randomForest_rb' not found
Error: object 'randomForest_wr' not found
Error: object 'randomForest_te' not found
Code
Error: object 'randomForest_qb' not found
Code
Error: object 'randomForest_rb' not found
Code
Error: object 'randomForest_wr' not found
Code
Error: object 'randomForest_te' not found
Error: object 'newData_seasonalQB_imp' not found
Error: object 'newData_seasonalRB_imp' not found
Error: object 'newData_seasonalWR_imp' not found
Error: object 'newData_seasonalTE_imp' not found
Code
Error: object 'newData_seasonalQB' not found
Code
Error: object 'newData_seasonalRB' not found
Code
Error: object 'newData_seasonalWR' not found
Code
Error: object 'newData_seasonalTE' not found
Code
Error: object 'newData_seasonalQB' not found
Code
Error: object 'newData_seasonalRB' not found
Code
Error: object 'newData_seasonalWR' not found
Code
Error: object 'newData_seasonalTE' not found
19.7.4.2 Longitudinal Data
Code
library("LongituRF")
smerf <- LongituRF::MERF(
X = seasonalData_subsetQB_imp$ximp[,c("passing_epa")] %>% as.matrix(),
Y = seasonalData_subsetQB$fantasyPoints_lag,
Z = seasonalData_subsetQB_imp$ximp[,c("pacr")] %>% as.matrix(),
id = seasonalData_subsetQB$gsis_id,
time = seasonalData_subsetQB_imp$ximp[,c("ageCentered20")] %>% as.matrix(),
ntree = 500,
sto = "BM")
smerf$forest # the fitted random forest (obtained at the last iteration)
smerf$random_effects # the predicted random effects for each player
smerf$omega # the predicted stochastic processes
plot(smerf$Vraisemblance) # evolution of the log-likelihood
smerf$OOB # OOB error at each iteration19.7.5 k-Fold Cross-Validation
19.7.6 Leave-One-Out (LOO) Cross-Validation
19.7.7 Combining Tree-Boosting with Mixed Models
To combine tree-boosting with mixed models, we use the gpboost package (gpboost?).
Adapted from here: https://towardsdatascience.com/mixed-effects-machine-learning-for-longitudinal-panel-data-with-gpboost-part-iii-523bb38effc
19.7.7.1 Process Data
If using a gamma distribution, it requires positive-only values:
19.7.7.2 Specify Predictor Variables
19.7.7.3 Specify General Model Options
19.7.7.4 Identify Optimal Tuning Parameters
For identifying the optimal tuning parameters for boosting, we partition the training data into inner training data and validation data. We randomly split the training data into 80% inner training data and 20% held-out validation data. We then use the mean absolute error as our index of prediction accuracy on the held-out validation data.
Code
# Partition training data into inner training data and validation data
ntrain_qb <- dim(data_train_qb_matrix)[1]
set.seed(52242)
valid_tune_idx_qb <- sample.int(ntrain_qb, as.integer(0.2*ntrain_qb)) #
folds_qb <- list(valid_tune_idx_qb)
# Specify parameter grid, gp_model, and gpb.Dataset
param_grid_qb <- list(
"learning_rate" = c(0.2, 0.1, 0.05, 0.01), # the step size used when updating predictions after each boosting round (high values make big updates, which can speed up learning but risk overshooting; low values are usually more accurate but require more rounds)
"max_depth" = c(3, 5, 7), # maximum depth (levels) of each decision tree; deeper trees capture more complex patterns and interactions but risk overfitting; shallower trees tend to generalize better
"min_data_in_leaf" = c(10, 50, 100), # minimum number of training examples in a leaf node; higher values = more regularization (simpler trees)
"lambda_l2" = c(0, 1, 5)) # L2 regularization penalty for large weights in tree splits; adds a "cost" for complexity; helps prevent overfitting by shrinking the contribution of each tree
other_params_qb <- list(
num_leaves = 2^6) # maximum number of leaves per tree; controls the maximum complexity of each tree (along with max_depth); more leaves = more expressive models, but can overfit if min_data_in_leaf is too small; num_leaves must be consistent with max_depth, because deeper trees naturally support more leaves; max is: 2^n, where n is the largest max_depth
gp_model_qb <- gpboost::GPModel(
group_data = data_train_qb_matrix[,"gsis_id"],
likelihood = model_likelihood,
group_rand_coef_data = cbind(
data_train_qb_matrix[,"ageCentered20"],
data_train_qb_matrix[,"ageCentered20Quadratic"]),
ind_effect_group_rand_coef = c(1,1))
gp_data_qb <- gpboost::gpb.Dataset(
data = data_train_qb_matrix[,pred_vars_qb],
categorical_feature = pred_vars_qb_categorical,
label = data_train_qb_matrix[,"fantasyPoints_lag"]) #use mean-centered variable and add mean back afterward
# Find optimal tuning parameters
opt_params_qb <- gpboost::gpb.grid.search.tune.parameters(
param_grid = param_grid_qb,
params = other_params_qb,
num_try_random = NULL,
folds = folds_qb,
data = gp_data_qb,
gp_model = gp_model_qb,
nrounds = nrounds,
early_stopping_rounds = 50, # stops training early if the model hasn’t improved on the validation set in 50 rounds; prevents overfitting and saves time
verbose_eval = 1,
metric = "mae")Error in fd$booster$update(fobj = fobj): [GPBoost] [Fatal] Inf occured in gradient wrt covariance / auxiliary parameter number 3 (counting starts at 1, total nb. par. = 4)
Error: object 'opt_params_qb' not found
A learning rate of 1 is very high for boosting. Even if a learning rate of 1 did well in tuning, I use a lower learning rate (0.1) to avoid overfitting. I also added some light regularization (lambda_l2) for better generalization. I also set the maximum tree depth (max_depth) at 5 to capture complex (up to 5-way) interactions, and set the maximum number of terminal nodes (num_leaves) per tree at 2^5 (32). I set the minimum number of samples in any leaf (min_data_in_leaf) to be 10.
19.7.7.5 Specify Model and Tuning Parameters
Code
gp_model_qb <- gpboost::GPModel(
group_data = data_train_qb_matrix[,"gsis_id"],
likelihood = model_likelihood,
group_rand_coef_data = cbind(
data_train_qb_matrix[,"ageCentered20"],
data_train_qb_matrix[,"ageCentered20Quadratic"]),
ind_effect_group_rand_coef = c(1,1))
gp_data_qb <- gpboost::gpb.Dataset(
data = data_train_qb_matrix[,pred_vars_qb],
categorical_feature = pred_vars_qb_categorical,
label = data_train_qb_matrix[,"fantasyPoints_lag"])
params_qb <- list(
learning_rate = 0.1,
max_depth = 5,
min_data_in_leaf = 10,
lambda_l2 = 1,
num_leaves = 2^5,
num_threads = num_cores)
nrounds_qb <- 123 # identify optimal number of trees through iteration and cross-validation
#gp_model_qb$set_optim_params(params = list(optimizer_cov = "nelder_mead")) # to speed up model estimation19.7.7.6 Fit Model
Code
[GPBoost] [Info] Total Bins 8709
[GPBoost] [Info] Number of data points in the train set: 1582, number of used features: 73
[GPBoost] [Info] [GPBoost with gamma likelihood]: initscore=4.805531
[GPBoost] [Info] Start training from score 4.805531
19.7.7.7 Model Results
=====================================================
Covariance parameters (random effects):
Param.
Group_1 0
Group_1_rand_coef_nb_1 0
Group_1_rand_coef_nb_2 0
-----------------------------------------------------
Additional parameters:
Param.
shape 0.8186
=====================================================
19.7.7.8 Evaluate Accuracy of Model on Test Data
Code
# Test Model on Test Data
pred_test_qb <- predict(
gp_model_fit_qb,
data = data_test_qb_matrix[,pred_vars_qb],
group_data_pred = data_test_qb_matrix[,"gsis_id"],
group_rand_coef_data_pred = cbind(
data_test_qb_matrix[,"ageCentered20"],
data_test_qb_matrix[,"ageCentered20Quadratic"]),
predict_var = FALSE,
pred_latent = FALSE)
y_pred_test_qb <- pred_test_qb[["response_mean"]] # if outcome is mean-centered, add mean(data_train_qb_matrix[,"fantasyPoints_lag"])
cbind(y_pred_test_qb, data_test_qb_matrix[,"fantasyPoints_lag"]) y_pred_test_qb
[1,] 128.741634 156.46
[2,] 76.493276 130.18
[3,] 86.580329 2.98
[4,] 41.918362 24.84
[5,] 37.188389 40.28
[6,] 62.495377 10.58
[7,] 30.746033 0.68
[8,] 30.473020 25.08
[9,] 20.828998 6.12
[10,] 23.109539 17.00
[11,] 26.812862 44.54
[12,] 93.304585 152.30
[13,] 130.223705 -0.10
[14,] 22.283134 137.96
[15,] 138.734733 154.78
[16,] 60.712951 7.64
[17,] 19.925267 6.10
[18,] 33.678771 228.66
[19,] 141.631493 207.44
[20,] 165.852806 23.80
[21,] 20.096552 263.06
[22,] 185.340278 157.30
[23,] 108.823427 174.48
[24,] 93.108431 228.56
[25,] 132.100496 75.36
[26,] 32.774043 6.72
[27,] 116.525878 75.06
[28,] 70.197255 173.40
[29,] 102.169202 161.88
[30,] 136.977511 81.36
[31,] 54.650312 19.86
[32,] 43.255479 74.86
[33,] 43.985011 48.92
[34,] 23.006372 97.48
[35,] 11.824330 32.84
[36,] 20.115555 -0.40
[37,] 73.908501 121.84
[38,] 83.489164 197.76
[39,] 102.369357 3.16
[40,] 20.873240 104.68
[41,] 44.745490 31.94
[42,] 34.736537 4.06
[43,] 14.407108 7.22
[44,] 159.000821 350.52
[45,] 241.187535 313.92
[46,] 236.021580 259.06
[47,] 222.324392 240.26
[48,] 94.955165 123.14
[49,] 80.164614 48.58
[50,] 17.991425 103.06
[51,] 58.973741 167.20
[52,] 61.609967 175.58
[53,] 59.976242 -0.20
[54,] 29.445815 71.82
[55,] 160.600030 244.56
[56,] 204.093650 156.12
[57,] 139.802683 222.18
[58,] 35.005865 17.78
[59,] 36.632469 1.54
[60,] 30.553265 134.74
[61,] 60.602463 182.74
[62,] 120.450158 177.76
[63,] 69.612526 14.66
[64,] 28.041788 19.84
[65,] 35.010957 150.30
[66,] 22.786721 44.56
[67,] 15.690009 40.26
[68,] 15.229177 86.84
[69,] 36.787024 5.46
[70,] 27.012087 43.82
[71,] 110.714314 303.70
[72,] 254.844284 271.52
[73,] 161.540020 235.56
[74,] 158.224152 230.12
[75,] 183.533516 310.10
[76,] 161.558170 165.78
[77,] 100.085016 201.68
[78,] 118.356555 219.56
[79,] 139.661832 255.66
[80,] 209.394948 248.32
[81,] 151.262323 193.18
[82,] 78.426242 66.94
[83,] 42.375312 44.54
[84,] 28.387321 11.04
[85,] 34.347125 67.98
[86,] 28.271807 6.12
[87,] 27.680009 12.52
[88,] 16.829451 -0.20
[89,] 42.286710 46.68
[90,] 37.455094 -0.10
[91,] 14.209401 9.26
[92,] 29.607459 -0.06
[93,] 16.339439 2.30
[94,] 34.811580 75.88
[95,] 45.060393 157.64
[96,] 101.488236 218.42
[97,] 136.011993 204.38
[98,] 107.216360 178.82
[99,] 90.485180 275.06
[100,] 116.542558 225.24
[101,] 120.004808 118.96
[102,] 57.158901 49.64
[103,] 8.450484 26.64
[104,] 40.680689 -0.10
[105,] 19.214051 18.02
[106,] 48.741939 35.82
[107,] 16.904948 -0.30
[108,] 37.288545 76.02
[109,] 38.168828 5.48
[110,] 54.013795 3.18
[111,] 39.121789 279.60
[112,] 11.259368 41.64
[113,] 68.275002 194.00
[114,] 121.789308 254.06
[115,] 154.077686 95.30
[116,] 72.317248 117.72
[117,] 69.504155 -0.10
[118,] 18.462864 3.00
[119,] 23.616444 25.82
[120,] 17.513915 2.68
[121,] 28.164915 115.54
[122,] 68.235021 0.20
[123,] 18.903275 -4.64
[124,] 19.013920 41.90
[125,] 37.628651 8.78
[126,] 40.910949 222.70
[127,] 151.389005 144.26
[128,] 113.212570 172.02
[129,] 137.332751 33.90
[130,] 23.393890 185.88
[131,] 100.050362 108.84
[132,] 46.834228 222.92
[133,] 137.834042 17.22
[134,] 29.570081 0.76
[135,] 15.108938 5.90
[136,] 25.744891 2.54
[137,] 22.627555 17.28
[138,] 11.101676 58.24
[139,] 25.133056 123.26
[140,] 66.157443 38.48
[141,] 13.568220 44.22
[142,] 44.336495 17.06
[143,] 25.996324 9.30
[144,] 14.510194 0.70
[145,] 31.883328 -0.30
[146,] 29.645612 11.16
[147,] 31.273725 7.86
[148,] 34.925507 5.62
[149,] 13.326815 1.26
[150,] 21.673501 3.12
[151,] 40.479096 0.02
[152,] 17.576464 51.52
[153,] 20.460485 0.66
[154,] 31.332930 80.12
[155,] 77.812542 156.14
[156,] 83.831779 103.18
[157,] 48.154191 3.50
[158,] 22.053486 86.94
[159,] 50.214249 -0.30
[160,] 22.118031 0.08
[161,] 23.073409 29.36
[162,] 60.378236 142.06
[163,] 122.367750 145.94
[164,] 67.252332 145.16
[165,] 71.689948 64.10
[166,] 28.294902 225.44
[167,] 57.008572 20.76
[168,] 40.510295 0.76
[169,] 18.775275 54.90
[170,] 44.524043 1.24
[171,] 25.292591 2.06
[172,] 27.039092 192.06
[173,] 42.881149 7.76
[174,] 32.373232 187.32
[175,] 150.387990 309.64
[176,] 192.397014 226.02
[177,] 152.404369 287.82
[178,] 196.015905 99.10
[179,] 61.859237 293.96
[180,] 197.685344 289.92
[181,] 198.362766 270.92
[182,] 161.876427 279.30
[183,] 181.418160 44.66
[184,] 32.246875 5.16
[185,] 53.026051 1.36
[186,] 26.739021 18.52
[187,] 24.259145 9.80
[188,] 45.619990 108.18
[189,] 14.431000 49.40
[190,] 45.116690 13.42
[191,] 16.549057 116.84
[192,] 69.821631 190.52
[193,] 93.082768 287.90
[194,] 181.951315 254.60
[195,] 161.991503 162.06
[196,] 63.900804 227.82
[197,] 140.313895 106.80
[198,] 58.216676 0.28
[199,] 32.436363 26.60
[200,] 23.917479 0.44
[201,] 17.931825 3.10
[202,] 12.186139 34.90
[203,] 38.300863 -0.40
[204,] 32.765254 20.94
[205,] 52.356832 228.48
[206,] 172.229067 193.86
[207,] 170.008860 208.34
[208,] 136.565427 202.52
[209,] 178.976431 249.34
[210,] 162.131195 245.08
[211,] 149.237032 294.82
[212,] 186.556782 238.92
[213,] 182.396547 176.32
[214,] 125.736532 277.50
[215,] 183.736196 303.38
[216,] 204.266926 232.18
[217,] 130.324223 207.32
[218,] 116.184853 252.96
[219,] 126.498297 57.38
[220,] 37.905933 7.78
[221,] 27.988110 10.96
[222,] 39.777551 22.32
[223,] 42.225725 68.06
[224,] 34.000295 1.50
[225,] 41.074557 0.08
[226,] 13.086861 5.20
[227,] 54.205994 7.14
[228,] 17.262576 -0.30
[229,] 15.169934 -0.40
[230,] 22.623265 11.40
[231,] 27.822707 14.52
[232,] 77.307391 183.14
[233,] 148.687232 46.46
[234,] 40.627936 148.50
[235,] 100.288020 138.80
[236,] 107.636519 224.66
[237,] 146.200980 128.68
[238,] 98.121358 263.22
[239,] 198.657426 228.00
[240,] 156.993125 277.24
[241,] 246.329016 238.78
[242,] 124.613120 305.18
[243,] 220.580058 147.00
[244,] 91.016938 75.58
[245,] 30.149301 11.04
[246,] 97.815396 30.08
[247,] 29.615726 13.06
[248,] 29.862823 10.80
[249,] 42.880602 6.18
[250,] 18.582752 2.60
[251,] 39.426320 0.36
[252,] 27.081655 40.58
[253,] 41.598284 17.22
[254,] 26.737657 -0.50
[255,] 21.471966 91.04
[256,] 50.240367 4.10
[257,] 45.432195 9.38
[258,] 27.146822 25.36
[259,] 22.802989 -2.04
[260,] 14.182438 46.14
[261,] 29.418591 71.48
[262,] 48.597351 105.70
[263,] 57.581424 88.76
[264,] 37.806320 86.30
[265,] 25.979047 8.66
[266,] 23.473261 60.50
[267,] 37.602489 95.74
[268,] 59.322552 -0.14
[269,] 26.926310 9.38
[270,] 33.732360 51.46
[271,] 32.902369 21.24
[272,] 36.290456 165.66
[273,] 131.064442 67.36
[274,] 33.637376 24.64
[275,] 20.878873 0.56
[276,] 14.406049 56.74
[277,] 26.377241 228.62
[278,] 97.597109 3.62
[279,] 31.198526 30.70
[280,] 38.089529 -0.20
[281,] 13.702492 1.10
[282,] 16.897648 0.64
[283,] 24.109093 6.34
[284,] 15.291694 3.32
[285,] 27.099736 68.88
[286,] 12.289169 16.50
[287,] 40.306380 11.36
[288,] 30.811033 1.54
[289,] 21.187629 6.08
[290,] 36.854653 0.58
[291,] 9.586886 15.80
[292,] 20.288053 40.20
[293,] 47.787870 163.94
[294,] 88.311608 172.64
[295,] 105.607589 86.60
[296,] 37.185148 68.88
[297,] 41.158467 -0.52
[298,] 18.341251 23.08
[299,] 31.616863 4.00
[300,] 31.711285 12.28
[301,] 34.345689 1.48
[302,] 23.597819 4.94
[303,] 33.000776 10.36
[304,] 124.891067 277.44
[305,] 276.204245 222.08
[306,] 133.652128 254.50
[307,] 193.993233 32.44
[308,] 40.784760 10.36
[309,] 23.957448 26.08
[310,] 33.239390 14.08
[311,] 41.439719 90.80
[312,] 10.741727 4.14
[313,] 23.364617 0.64
[314,] 40.466157 15.82
[315,] 22.240615 35.16
[316,] 27.247508 8.72
[317,] 24.145373 1.36
[318,] 16.520377 -0.06
[319,] 52.035577 52.34
[320,] 42.698605 -0.10
[321,] 20.081118 10.30
[322,] 16.811510 3.60
[323,] 5.731763 7.40
[324,] 46.571609 7.30
[325,] 15.133207 10.80
[326,] 28.142495 6.30
[327,] 26.298198 1.00
[328,] 29.664469 19.64
[329,] 131.687161 105.16
[330,] 50.415712 238.48
[331,] 192.839895 122.58
[332,] 83.087206 209.90
[333,] 158.465827 237.88
[334,] 158.802879 26.98
[335,] 28.543762 16.70
[336,] 25.201194 184.74
[337,] 294.399300 335.46
[338,] 286.936554 303.66
[339,] 283.207946 266.98
[340,] 194.034487 402.08
[341,] 284.085081 261.26
[342,] 184.420419 308.98
[343,] 235.617287 284.60
[344,] 254.053458 21.68
[345,] 48.701302 268.98
[346,] 154.391063 90.36
[347,] 39.677908 151.42
[348,] 85.958124 142.14
[349,] 147.934323 103.74
[350,] 73.762001 69.92
[351,] 29.167055 14.52
[352,] 37.297271 182.06
[353,] 154.307424 277.28
[354,] 246.460310 266.66
[355,] 212.461996 116.20
[356,] 68.500815 213.44
[357,] 127.057103 103.92
[358,] 35.410808 7.42
[359,] 17.959288 3.52
[360,] 11.116868 0.56
[361,] 17.493820 24.80
[362,] 10.795376 43.02
[363,] 33.196895 150.30
[364,] 19.024410 1.76
[365,] 24.762455 21.44
[366,] 37.343413 24.48
[367,] 36.697686 6.32
[368,] 43.181861 54.44
[369,] 20.101485 0.04
[370,] 16.767578 64.58
[371,] 125.986092 93.64
[372,] 36.723727 20.02
[373,] 49.948221 68.42
[374,] 49.353231 -0.10
[375,] 28.406756 30.32
[376,] 134.429972 256.32
[377,] 165.478621 294.50
[378,] 197.385257 278.32
[379,] 197.815050 202.20
[380,] 151.141117 151.96
[381,] 68.605926 234.18
[382,] 108.453988 352.36
[383,] 228.238143 280.86
[384,] 213.589369 167.24
[385,] 118.522178 85.04
[386,] 39.168380 -0.20
[387,] 40.377452 0.72
[388,] 20.339467 -1.46
[389,] 66.706760 6.46
[390,] 34.642560 11.68
[391,] 22.835408 1.70
[392,] 20.856311 30.32
[393,] 23.503427 0.76
[394,] 7.723413 6.72
[395,] 26.252434 12.16
[396,] 18.913424 19.40
[397,] 22.684451 0.00
[398,] 18.947548 14.52
[399,] 22.801240 102.00
[400,] 94.982190 122.04
[401,] 12.241181 196.74
[402,] 113.067567 132.10
[403,] 50.474916 0.12
[404,] 16.840156 94.16
[405,] 41.287889 10.16
[406,] 21.782455 34.96
[407,] 23.833366 8.56
[408,] 25.434350 -0.48
[409,] 83.461217 18.80
[410,] 38.138719 28.00
[411,] 189.927323 17.98
[412,] 50.768424 -3.24
[413,] 20.242938 1.80
[414,] 14.520171 -1.90
[415,] 21.928831 16.80
[416,] 16.346178 0.38
[417,] 12.478261 0.00
[418,] 38.724728 26.02
[419,] 18.810524 8.78
[420,] 12.306305 0.20
Code
19.7.7.9 Generate Predictions for Next Season
Code
# Generate model predictions for next season
pred_nextYear_qb <- predict(
gp_model_fit_qb,
data = newData_qb_matrix[,pred_vars_qb],
group_data_pred = newData_qb_matrix[,"gsis_id"],
group_rand_coef_data_pred = cbind(
newData_qb_matrix[,"ageCentered20"],
newData_qb_matrix[,"ageCentered20Quadratic"]),
predict_var = FALSE,
pred_latent = FALSE)
newData_qb$fantasyPoints_lag <- pred_nextYear_qb$response_mean
# Merge with player names
newData_qb <- left_join(
newData_qb,
nfl_playerIDs %>% select(gsis_id, name),
by = "gsis_id"
)
newData_qb %>%
arrange(-fantasyPoints_lag) %>%
select(name, fantasyPoints_lag, fantasyPoints)19.8 Conclusion
19.9 Session Info
R version 4.5.1 (2025-06-13)
Platform: x86_64-pc-linux-gnu
Running under: Ubuntu 24.04.2 LTS
Matrix products: default
BLAS: /usr/lib/x86_64-linux-gnu/openblas-pthread/libblas.so.3
LAPACK: /usr/lib/x86_64-linux-gnu/openblas-pthread/libopenblasp-r0.3.26.so; LAPACK version 3.12.0
locale:
[1] LC_CTYPE=C.UTF-8 LC_NUMERIC=C LC_TIME=C.UTF-8
[4] LC_COLLATE=C.UTF-8 LC_MONETARY=C.UTF-8 LC_MESSAGES=C.UTF-8
[7] LC_PAPER=C.UTF-8 LC_NAME=C LC_ADDRESS=C
[10] LC_TELEPHONE=C LC_MEASUREMENT=C.UTF-8 LC_IDENTIFICATION=C
time zone: UTC
tzcode source: system (glibc)
attached base packages:
[1] parallel stats graphics grDevices utils datasets methods
[8] base
other attached packages:
[1] lubridate_1.9.4 forcats_1.0.0 stringr_1.5.1 dplyr_1.1.4
[5] purrr_1.0.4 readr_2.1.5 tidyr_1.3.1 tibble_3.3.0
[9] tidyverse_2.0.0 gpboost_1.5.8 R6_2.6.1 caret_7.0-1
[13] lattice_0.22-7 ggplot2_3.5.2 powerjoin_0.1.0 missRanger_2.6.1
[17] doParallel_1.0.17 iterators_1.0.14 foreach_1.5.2 petersenlab_1.1.5
loaded via a namespace (and not attached):
[1] DBI_1.2.3 mnormt_2.1.1 pROC_1.18.5
[4] gridExtra_2.3 rlang_1.1.6 magrittr_2.0.3
[7] compiler_4.5.1 vctrs_0.6.5 reshape2_1.4.4
[10] quadprog_1.5-8 pkgconfig_2.0.3 fastmap_1.2.0
[13] backports_1.5.0 pbivnorm_0.6.0 rmarkdown_2.29
[16] prodlim_2025.04.28 tzdb_0.5.0 xfun_0.52
[19] jsonlite_2.0.0 recipes_1.3.1 psych_2.5.6
[22] lavaan_0.6-19 cluster_2.1.8.1 stringi_1.8.7
[25] RColorBrewer_1.1-3 ranger_0.17.0 parallelly_1.45.0
[28] rpart_4.1.24 Rcpp_1.0.14 knitr_1.50
[31] future.apply_1.20.0 base64enc_0.1-3 FNN_1.1.4.1
[34] Matrix_1.7-3 splines_4.5.1 nnet_7.3-20
[37] timechange_0.3.0 tidyselect_1.2.1 rstudioapi_0.17.1
[40] yaml_2.3.10 timeDate_4041.110 codetools_0.2-20
[43] listenv_0.9.1 plyr_1.8.9 withr_3.0.2
[46] evaluate_1.0.4 foreign_0.8-90 future_1.58.0
[49] survival_3.8-3 pillar_1.10.2 checkmate_2.3.2
[52] stats4_4.5.1 generics_0.1.4 mix_1.0-13
[55] hms_1.1.3 scales_1.4.0 globals_0.18.0
[58] xtable_1.8-4 class_7.3-23 glue_1.8.0
[61] Hmisc_5.2-3 tools_4.5.1 data.table_1.17.6
[64] ModelMetrics_1.2.2.2 gower_1.0.2 mvtnorm_1.3-3
[67] grid_4.5.1 mitools_2.4 ipred_0.9-15
[70] colorspace_2.1-1 nlme_3.1-168 RJSONIO_2.0.0
[73] htmlTable_2.4.3 Formula_1.2-5 cli_3.6.5
[76] viridisLite_0.4.2 lava_1.8.1 gtable_0.3.6
[79] digest_0.6.37 htmlwidgets_1.6.4 farver_2.1.2
[82] htmltools_0.5.8.1 lifecycle_1.0.4 hardhat_1.4.1
[85] MASS_7.3-65
